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Lesson 3: Basic Descriptive Statistics
7 Calculating the Variance < Back | Next >

The variance provides a description of how spread out the data you collected is. The variance is computed as the average squared deviation of each number from its mean. Mathematically speaking the formula looks like this:

Where M is equal to the mean of the data, and N is equal to the number of data points.

Example

To better show you how to calculate the variance we will now go over an example. Let’s assume the following 4 data points represent trees per acre of our sample points for a potential treatment area.

156, 176, 184, 209

We would all agree that the range of this data is 53 trees per acre, and the mean is equal to about 181 trees per acre. We now need to calculate the variance. You can begin by subtracting the mean from each value and then squaring the result as shown below:

(156 – 181)2 = 625
(176 – 181)2 = 25
(184 - 181)2 = 9
(209 - 181)2 = 784

The next step is to add together the results. You should get 1443
Last you divide this number by the number of sample points minus 1. You should end up with the following solution:

S2 = 481

Calculating the variance is important for many other statistical calculations. So it is important that you have a basic understanding of how this value is calculated. It is also the first step in calculating the standard deviation.

The following three data points are the flow rates for three streams in a given watershed in cubic feet per second:
106, 125, 202

The mean for the data is equal to 144.3 cubic feet per second, and the number of samples is equal to 3

What is the variance for this data set?
A. 96
B. 9216.5
C. 2544.4
D. 1124.7

Response:

LESSON 3
1 Overview
2 Intro to Descriptive Statistics
3 Calculating the Mean or Average
4 Calculating the Median
5 Calculating the Mode
6 Describing the Spread of Data
7 Calculating the Variance
8 Calculating the Standard Deviation
9 Graphical Representation of Data
10 The Stem and Leaf Plot
11 Review Questions
< Back | Next >

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